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The MOLGEN Chemical Identifier MOLGEN-CID is a software module freely accessible via the Internet. For a molecule or graph entered in molfile format (2D) it produces, by a canonical renumbering procedure, a canonical molfile and a unique character string that is easily compared by computer to a similar string. The mode of operation of MOLGEN-CID is detailed and visualized with examples.
A recurrent problem in organic chemistry is the generation of new molecular structures that conform to some predetermined set of structural constraints that are imposed in an endeavor to build certain required properties into the newly generated structure. An example of this is the pharmacophore model, used in medicinal chemistry to guide de novo design or selection of suitable structures from compound databases. We propose here a method that efficiently links up a selected number of required atom positions while at the same time directing the emergent molecular skeleton to avoid forbidden positions. The linkage process takes place on a lattice whose unit step length and overall geometry is designed to match typical architectures of organic molecules. We use an optimization method to select from the many different graphs possible. The approach is demonstrated in an example where crystal structures of the same (in this case rigid) ligand complexed with different proteins are available.
The great size of chemical databases and the high computational cost required in the atom-atom comparison of molecular structures for the calculation of the similarity between two chemical compounds necessitate the proposal of new clustering models with the aim of reducing the time of recovery of a set of molecules from a database that satisfies a range of similarities with regard to a given molecule pattern. In this paper we make use of the information corresponding to the cycles existing in the structure of molecules as an approach for the classification of chemical databases. The clustering method here proposed is based on the representation of the topological structure of molecules stored in chemical databases through its corresponding cycle graph. This method presents a more appropriate behavior for others described in the bibliography in which the information corresponding to the cyclicity of the molecules is also used.
The support vector machine algorithm together with graph kernel functions has recently been introduced to model structure-activity relationships (SAR) of molecules from their 2D structure, without the need for explicit molecular descriptor computation. We propose two extensions to this approach with the double goal to reduce the computational burden associated with the model and to enhance its predictive accuracy: description of the molecules by a Morgan index process and definition of a second-order Markov model for random walks on 2D structures. Experiments on two mutagenicity data sets validate the proposed extensions, making this approach a possible complementary alternative to other modeling strategies.
Relational databases are the current standard for storing and retrieving data in the pharmaceutical and biotech industries. However, retrieving data from a relational database requires specialized knowledge of the database schema and of the SQL query language. At Anadys, we have developed an easy-to-use system for searching and reporting data in a relational database to support our drug discovery project teams. This system is fast and flexible and allows users to access all data without having to write SQL queries. This paper presents the hierarchical, graph-based metadata representation and SQL-construction methods that, together, are the basis of this system's capabilities.
In the pharmaceutical industry, the virtual screening of combinatorial libraries is used to rationally select compounds for biological testing from databases of hundreds of thousands of compounds. In addition to structural descriptors, such as fingerprints and pharmacophores, the application of relatively simple structural descriptors traditionally used in quantitative structure-activity studies offers speed and efficiency for rapidly measuring the molecular diversity of such collections. We explore new topological indices computed from the molecular graph as potential structural descriptors for the characterization of molecular diversity. A database of 2000 compounds randomly selected from the National Cancer Institute AIDS database was used to measure the intercorrelation of the descriptors. The initial collection of 240 structural descriptors was reduced to several quasi-orthogonal sets of up to 9 descriptors, using different thresholds for the maximum intercorrelation coefficient.
There is an abundance of structural molecular descriptors of various forms that have been proposed and tested over the years. Very often different descriptors represent, more or less, the same aspects of molecular structures and, thus, they have diminished discriminating power for the identification of different structural features that might contribute to the molecular property, or activity of interest. Therefore, it is essential that noncorrelated descriptors be employed to ensure the wider and the less inflated possible coverage of the chemical space. The most usual approach for reducing the number of descriptors and employing noncorrelated (or orthogonal) descriptors involves principal component analysis (PCA) or other factor analytical techniques. In this work we present an approach for determining relationships (groupings) among 240 graph-theoretical descriptors, as a means for selecting nonredundant ones, based on the application of cluster analysis (CA). To remove inherent biases and particularities of different CA algorithms, several clustering solutions, using these algorithms, were "hybridized" to obtain a reliable and confident overall solution concerning how the interrelationships within the data are structured. The calculated correlation coefficients between descriptors were used as a reference for a discussion on the different CA methods employed, and the resulted clusters of descriptors were statistically analyzed for deriving the intercorrelations between the different operators, weighting schemes and matrices used for the computation of these descriptors.
A doubly fused tricyclic polymer architecture, corresponding to a delta-graph, has been constructed effectively through metathesis polymer cyclization (MPC) of an 8-shaped dicyclic polymer precursor having two allyl groups placed at opposite positions of the two rings of the 8-shaped structure. The 8-shaped polymer precursor has been obtained through the covalent conversion of an electrostatic self-assembly (composed of two units of the linear poly(tetrahydrofuran)s, poly(THF)s, having pyrrolidinium salt end groups and having a pendant allyl group at the middle of the chain, carrying a tetrafunctional carboxylate counteranion) by the heating treatment under appropriate dilution to cause the ring-opening reaction of pyrrolidinium salt groups by carboxylate anions.
We develop a method for calculating the exact free energy of tree clusters formed from associating telechelic molecules. The method uses the concept of rooted trees from the graph theory to enumerate all topologically distinct trees having a maximum degree of branching; it recursively separates the trees into different classes based on their connectivity, thus enabling the exact summation of the trees weighted by their respective Boltzmann factors. We apply our method to studying the pregel properties in pure telechelic solutions and in mixed telechelic and single-associating-end polymer solutions. We highlight the effect of energetic tendency for branching in the former and the effect of competitive association in the latter.
A novel approach to computer-aided molecular design is illustrated. This approach is based on the calculation of the spectral moments of the bond adjacency matrix of graphs representing molecular structures. Spectral moments are then expressed as linear combinations of the different sub-structures present in molecules. Two series of compounds, one containing sedative/hypnotic and the other containing different classes of drugs were used to find a discriminant function with the present approach. Several compounds from the Merck Index were identified by the model as sedative/hypnotic, five of them were found in the recent literature as possessing this activity. The critical fragments, actives and inactive ones, were detected.
Sufficient conditions for existence of concentration oscillations of components of complex reactions are considered on the basis of graph theory. Graphical rules were developed for detecting oscillators in kinetic schemes of complex biochemical systems. The main types of topology and principles of construction of kinetic schemes of oscillators containing two, three, and four substances are considered. The resulting oscillators might be a part of the biochemical systems of the n-th order. Under certain conditions they were found to be capable of generating oscillations of the system components.
Confounding, a special type of bias, occurs when an extraneous factor is associated with the exposure and independently affects the outcome. In order to get an unbiased estimate of the exposure-outcome relationship, we need to identify potential confounders, collect information on them, design appropriate studies, and adjust for confounding in data analysis. However, it is not always clear which variables to collect information on and adjust for in the analyses. Inappropriate adjustment for confounding can even introduce bias where none existed. Directed acyclic graphs (DAGs) provide a method to select potential confounders and minimize bias in the design and analysis of epidemiological studies. DAGs have been used extensively in expert systems and robotics. Robins (1987) introduced the application of DAGs in epidemiology to overcome shortcomings of traditional methods to control for confounding, especially as they related to unmeasured confounding. DAGs provide a quick and visual way to assess confounding without making parametric assumptions. We introduce DAGs, starting with definitions and rules for basic manipulation, stressing more on applications than theory. We then demonstrate their application in the control of confounding through examples of observational and cross-sectional epidemiological studies.
Recent mammalian microarray experiments detected widespread transcription and indicated that there may be many undiscovered multiple-exon protein-coding genes. To explore this possibility, we labeled cDNA from unamplified, polyadenylation-selected RNA samples from 37 mouse tissues to microarrays encompassing 1.14 million exon probes. We analyzed these data using GenRate, a Bayesian algorithm that uses a genome-wide scoring function in a factor graph to infer genes. At a stringent exon false detection rate of 2.7%, GenRate detected 12,145 gene-length transcripts and confirmed 81% of the 10,000 most highly expressed known genes. Notably, our analysis showed that most of the 155,839 exons detected by GenRate were associated with known genes, providing microarray-based evidence that most multiple-exon genes have already been identified. GenRate also detected tens of thousands of potential new exons and reconciled discrepancies in current cDNA databases by 'stitching' new transcribed regions into previously annotated genes.
A graph-theoretic technique using spanning trees is described for the evaluation of Flux Control Coefficients of metabolic pathways. The technique is illustrated by investigating a linear pathway (a) in the absence of feedback and feedforward regulation. (b) with its first enzyme inhibited by the end product and (c) with multiple feedback loops. It is shown that the Flux Control Coefficients of a linear pathway with one or more feedback loops can be derived in a systematic manner by superimposing the effect of the feedback loop(s) on the expressions pertaining to the Flux Control Coefficients of the unregulated pathway.
Heterogeneous surface reactions exhibiting complex spatiotemporal dynamics and patterns can be studied as processes involving reaction-diffusion mechanisms. In many realistic situations, the surface has fractal characteristics. This situation is studied by isometric graphing and multidimensional scaling (IGMDS) of fractal surfaces for extracting geodesic distances (i.e., shortest scaled distances that obtain edges of neighboring surface nodes and their interconnections) and the results obtained used to model effects of surface diffusion with nonlinear reactions. Further analysis of evolved spatiotemporal patterns may be carried out by IGMDS because high-dimensional snapshot data can be efficiently projected to a transformed subspace with reduced dimensions. Validation of the IGMDS methodology is carried out by comparing results with reduction capabilities of conventional principal component analysis for simple situations of reaction and diffusion on surfaces. The usefulness of the IGMDS methodology is shown for analysis of complex patterns formed on both regular and fractal surfaces, and using generic nonlinear reaction-diffusion systems following FitzHugh Nagumo and cubic reaction kinetics. The studies of these systems with nonlinear kinetics and noise show that effects of surface disorder due to fractality can become very relevant. The relevance is shown by studying properties of dynamical invariants in IGMDS component space, viz., the Lyapunov exponents and the KS entropy for interesting situations of spiral formation and turbulent patterns.
Interaction networks are of central importance in postgenomic molecular biology, with increasing amounts of data becoming available by high-throughput methods. Examples are gene regulatory networks or protein interaction maps. The main challenge in the analysis of these data is to read off biological functions from the topology of the network. Topological motifs, i.e., patterns occurring repeatedly at different positions in the network, have recently been identified as basic modules of molecular information processing. In this article, we discuss motifs derived from families of mutually similar but not necessarily identical patterns. We establish a statistical model for the occurrence of such motifs, from which we derive a scoring function for their statistical significance. Based on this scoring function, we develop a search algorithm for topological motifs called graph alignment, a procedure with some analogies to sequence alignment. The algorithm is applied to the gene regulation network of Escherichia coli.
We prove that any finite undirected graph can be canonically embedded isometrically into a maximum cartesian product of irreducible factors.
After a review of the diagram method for continuous-time random walks on graphs with cycles, the method is extended to discrete-time random walks. The basic theorems carry over formally from continuous time to discrete time. Three problems in tennis probabilities are used to illustrate random walks on discrete-time diagrams with cycles.